This would, although it appears in a conditional, is not used in the ordinary predictive sense but in a "volitive" sense fossilized from the original meaning of will = want, desire, be willing.
This survives mostly as a "past subjunctive" in such polite questions as your example, where it means, approximately, "please", and in earnest wishes such as
If he would only listen to me! .. that is, "I wish he were willing to listen."
It does survive in present-tense form as well in such "negotiating" constructions as this:
If you'll find me the saw I'll cut that for you.
Will in the condition clause marks this as a different sense than your ordinary "first conditional".